Convert a number range to another range maintaining ratio

Question

I m trying to convert one range of numbers to another  maintaining ratio  Maths is not my strong point   I have an image file where point values may range from -16000 00 to 16000 00 though the typical range may be much less  What I want to do is compress these values into the integer range 0-100  where 0 is the value of the smallest point  and 100 is the value of the largest  All points in between should keep a relative ratio even though some precision is being lost I d like to do this in python but even a general algorithm should suffice  I d prefer an algorithm where the min max or either range can be adjusted  ie  the second range could be -50 to 800 instead of 0 to 100

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Short-cut simplified proposal    NewRange OldRange   Handy multiplicand or HM  Convert OldValue in OldRange to NewValue in NewRange      OldValue - OldMin x HM    NewMin   wayne

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List comprehension one liner solution  color array new    int    x - min node sizes     99     max node sizes  - min node sizes      1  for x in node sizes    Longer version  def colour specter waste amount   color array      OldRange   max waste amount  - min waste amount  NewRange   99 for number value in waste amount      NewValue   int    number value - min waste amount     NewRange    OldRange    1      color array append NewValue  print color array  return color array

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This example converts a songs current position into an angle range of 20 - 40              lt summary gt          This test converts Current songtime to an angle in a range            lt  summary gt       Fact      public void ConvertRangeTests                              Convert a songs time to an angle of a range 20 - 40         var result   ConvertAndGetCurrentValueOfRange              TimeSpan Zero  TimeSpan FromMinutes 5 4               20  40               2 7                         Assert True result    30                   lt summary gt          Gets the current value from the mixValue maxValue range                   lt  summary gt           lt param name  startTime  gt Start of the song lt  param gt           lt param name  duration  gt  lt  param gt           lt param name  minValue  gt  lt  param gt           lt param name  maxValue  gt  lt  param gt           lt param name  value  gt Current time lt  param gt           lt returns gt  lt  returns gt      public double ConvertAndGetCurrentValueOfRange                  TimeSpan startTime                  TimeSpan duration                  double minValue                  double maxValue                  double value                var timeRange   duration - startTime          var newRange   maxValue - minValue          var ratio   newRange   timeRange TotalMinutes          var newValue   value   ratio          var currentValue  newValue   minValue          return currentValue

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Here is a Javascript version that returns a function that does the rescaling for predetermined source and destination ranges  minimizing the amount of computation that has to be done each time      This function returns a function bound to the     min max source  amp  target ranges given     oMin  oMax   source    nMin  nMax   dest  function makeRangeMapper oMin  oMax  nMin  nMax          range check     if  oMin    oMax           console log  Warning  Zero input range            return undefined              if  nMin    nMax           console log  Warning  Zero output range            return undefined              check reversed input range     var reverseInput   false      let oldMin   Math min  oMin  oMax        let oldMax   Math max  oMin  oMax        if  oldMin    oMin           reverseInput   true               check reversed output range     var reverseOutput   false        let newMin   Math min  nMin  nMax       let newMax   Math max  nMin  nMax       if  newMin    nMin           reverseOutput   true                Hot-rod the most common case      if   reverseInput  amp  amp   reverseOutput            let dNew   newMax-newMin          let dOld   oldMax-oldMin          return  x   gt               return   x-oldMin   dNew   dOld    newMin                       return  x   gt           let portion          if  reverseInput               portion    oldMax-x   newMax-newMin   oldMax-oldMin             else               portion    x-oldMin   newMax-newMin   oldMax-oldMin                    let result          if  reverseOutput               result   newMax - portion            else               result   portion   newMin                     return result               Here is an example of using this function to scale 0-1 into -0x80000000  0x7FFFFFFF  let normTo32Fn   makeRangeMapper 0  1  -0x80000000  0x7FFFFFFF   let fs   normTo32Fn 0 5   let fs2   normTo32Fn 0

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C   Variant  I found PenguinTD s Solution usefull  so i ported it to C   if anyone needs it      float remap float x  float oMin  float oMax  float nMin  float nMax       range check if  oMin    oMax          std  cout lt  lt   Warning  Zero input range       return -1        if  nMin    nMax         std  cout lt  lt  Warning  Zero output range       return -1              check reversed input range bool reverseInput   false  float oldMin   min  oMin  oMax    float oldMax   max  oMin  oMax    if  oldMin    oMin      reverseInput   true     check reversed output range bool reverseOutput   false    float newMin   min  nMin  nMax    float newMax   max  nMin  nMax    if  newMin    nMin      reverseOutput   true   float portion    x-oldMin   newMax-newMin   oldMax-oldMin   if  reverseInput      portion    oldMax-x   newMax-newMin   oldMax-oldMin    float result   portion   newMin  if  reverseOutput      result   newMax - portion   return result

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I wrote a function to do this in R  The method is the same as above  but I needed to do this a bunch of times in R  so I thought I d share in case it helps anybody  convertRange  lt - function    oldValue    oldRange   c -16000 00  16000 00      newRange   c 0  100     returnInt   TRUE   the poster asked for an integer  so this is an option      oldMin  lt - oldRange 1    oldMax  lt - oldRange 2    newMin  lt - newRange 1    newMax  lt - newRange 2    newValue      oldValue - oldMin    newMax - newMin      oldMax - oldMin     newMin      if returnInt      return round newValue       else      return newValue

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In the listing provided by PenguinTD  I do not understand why the ranges are reversed  it works without having to reverse the ranges  Linear range conversion is based upon the linear equation Y Xm n  where m and n are derived from the given ranges  Rather than refer to the ranges as min and max  it would be better to refer to them as 1 and 2  So the formula would be   Y      X - x1     y2 - y1      x2 - x1     y1   Where Y y1 when X x1  and Y y2 when X x2  x1  x2  y1  amp  y2 can be given any positive or negative value  Defining the expression in a macro makes it more useful it can then be used with any argument names    define RangeConv X  x1  x2  y1  y2     float   X - x1     y2 - y1      x2 - x1     y1    The float cast would ensure floating point division in the case where all the arguments are integer values  Depending on the application it may not be necessary to check the ranges x1 x2 and y1  y2

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I used this solution in a problem I was solving in js  so I thought I would share the translation  Thanks for the explanation and solution   function remap  x  oMin  oMax  nMin  nMax      range check if  oMin    oMax       console log  Warning  Zero input range        return None      if  nMin    nMax       console log  Warning  Zero output range        return None      check reversed input range var reverseInput   false  oldMin   Math min  oMin  oMax    oldMax   Math max  oMin  oMax    if  oldMin    oMin       reverseInput   true       check reversed output range var reverseOutput   false    newMin   Math min  nMin  nMax   newMax   Math max  nMin  nMax   if  newMin    nMin       reverseOutput   true      var portion    x-oldMin   newMax-newMin   oldMax-oldMin  if  reverseInput       portion    oldMax-x   newMax-newMin   oldMax-oldMin       var result   portion   newMin if  reverseOutput       result   newMax - portion     return result

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I personally use the helper class which supports generics  Swift 3  4 x compatible  struct Rescale lt Type   BinaryFloatingPoint gt        typealias RescaleDomain    lowerBound  Type  upperBound  Type       var fromDomain  RescaleDomain     var toDomain  RescaleDomain      init from  RescaleDomain  to  RescaleDomain            self fromDomain   from         self toDomain   to            func interpolate   x  Type   - gt  Type           return self toDomain lowerBound    1 - x    self toDomain upperBound   x             func uninterpolate   x  Type  - gt  Type           let b    self fromDomain upperBound - self fromDomain lowerBound     0   self fromDomain upperBound - self fromDomain lowerBound   1   self fromDomain upperBound          return  x - self fromDomain lowerBound    b            func rescale   x  Type    - gt  Type           return interpolate  uninterpolate x             Ex     let rescaler   Rescale lt Float gt  from   -1  1   to   0  100           print rescaler rescale 0      OUTPUT  50

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NewValue      OldValue - OldMin     NewMax - NewMin      OldMax - OldMin     NewMin   Or a little more readable     OldRange    OldMax - OldMin    NewRange    NewMax - NewMin    NewValue      OldValue - OldMin    NewRange    OldRange    NewMin   Or if you want to protect for the case where the old range is 0  OldMin   OldMax    OldRange    OldMax - OldMin  if  OldRange    0      NewValue   NewMin else       NewRange    NewMax - NewMin        NewValue      OldValue - OldMin    NewRange    OldRange    NewMin     Note that in this case we re forced to pick one of the possible new range values arbitrarily  Depending on context  sensible choices could be  NewMin  see sample   NewMax or  NewMin   NewMax    2

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Added KOTLIN version with Mathematical Explanation Consider we have a scale between  OMin  Omax  and we we have a value X in this range We want to convert it to scale   NMin  NMax  We know X and we need to find Y  the ratio must be same     gt   Y-NMin   NMax-NMin     X-OMin   OMax-OMin              gt    Y-NMin  NewRange    X-OMin  OldRange      gt    Y     X-OMin  NewRange  oldRange  NMin  Answer      Pragmatically we can write this rquation like this   private fun  convertScale oldValueToConvert Int   Float             Old Scale 50-100        val oldScaleMin   50        val oldScaleMax   100        val oldScaleRange   oldScaleMax - oldScaleMin            new Scale 0-1        val newScaleMin   0 0f        val newScaleMax   1 0f        val newScaleRange    newScaleMax - newScaleMin               return   oldValueToConvert - oldScaleMin   newScaleRange  oldScaleRange    newScaleMin        JAVA                     param x         param inMin         param inMax         param outMin         param outMax         return                 private long normalize long x  long inMin  long inMax  long outMin  long outMax              long outRange   outMax - outMin            long inRange    inMax - inMin            return  x - inMin   outRange   inRange   outMin             Usage  float brightness   normalize progress  0  10  0 255

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PHP Port  Found PenguinTD s solution helpful so I ported it to PHP  Help yourself                                                              Remap Range                                                       - Convert one range to another   including value       param    int  intValue   The value in the old range you wish to convert    param    int  oMin       The minimum of the old range    param    int  oMax       The maximum of the old range    param    int  nMin       The minimum of the new range    param    int  nMax       The maximum of the new range      return   float  fResult  The old value converted to the new range    function remapRange  intValue   oMin   oMax   nMin   nMax           Range check     if   oMin     oMax            echo  Warning  Zero input range           return false             if   nMin     nMax            echo  Warning  Zero output range           return false                Check reversed input range      bReverseInput   false       intOldMin   min  oMin   oMax        intOldMax   max  oMin   oMax       if   intOldMin     oMin             bReverseInput   true                Check reversed output range      bReverseOutput   false       intNewMin   min  nMin   nMax        intNewMax   max  nMin   nMax       if   intNewMin     nMin             bReverseOutput   true              fRatio     intValue -  intOldMin      intNewMax -  intNewMin      intOldMax -  intOldMin       if   bReverseInput             fRatio     intOldMax -  intValue      intNewMax -  intNewMin      intOldMax -  intOldMin               fResult    fRatio    intNewMin      if   bReverseOutput             fResult    intNewMax -  fRatio             return  fResult

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Actually there are some cases that above answers would break  Such as wrongly input value  wrongly input range  negative input output ranges   def remap  x  oMin  oMax  nMin  nMax          range check     if oMin    oMax          print  Warning  Zero input range          return None      if nMin    nMax          print  Warning  Zero output range          return None       check reversed input range     reverseInput   False     oldMin   min  oMin  oMax       oldMax   max  oMin  oMax       if not oldMin    oMin          reverseInput   True       check reversed output range     reverseOutput   False        newMin   min  nMin  nMax       newMax   max  nMin  nMax       if not newMin    nMin           reverseOutput   True      portion    x-oldMin   newMax-newMin   oldMax-oldMin      if reverseInput          portion    oldMax-x   newMax-newMin   oldMax-oldMin       result   portion   newMin     if reverseOutput          result   newMax - portion      return result   test cases print remap  25 0  0 0  100 0  1 0  -1 0          0 5 print remap  25 0  100 0  -100 0  -1 0  1 0          -0 25 print remap  -125 0  -100 0  -200 0  1 0  -1 0          0 5 print remap  -125 0  -200 0  -100 0  -1 0  1 0          0 5  even when value is out of bound print remap  -20 0  0 0  100 0  0 0  1 0          -0 2

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I didn t dig up the BNF for this  but the Arduino documentation had a great example of the function and it s breakdown  I was able to use this in Python by simply adding a def renaming to remap  cause map is a built-in  and removing the type casts and curly braces  ie just remove all the  long s    Original  long map long x  long in min  long in max  long out min  long out max      return  x - in min     out max - out min     in max - in min    out min      Python  def remap x  in min  in max  out min  out max     return  x - in min     out max - out min     in max - in min    out min   https   www arduino cc en reference map

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Here s some short Python functions for your copy and paste ease  including a function to scale an entire list   def scale number unscaled  to min  to max  from min  from max       return  to max-to min   unscaled-from min   from max-from min  to min  def scale list l  to min  to max       return  scale number i  to min  to max  min l   max l   for i in l    Which can be used like so   scale list  1 3 4 5   0  100        0 0  50 0  75 0  100 0    In my case I wanted to scale a logarithmic curve  like so   scale list  math log i 1  for i in range 5    0  50        0 0  21 533827903669653  34 130309724299266  43 06765580733931  50 0

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Java Version  Always works no matter what you feed it   I left everything expanded out so that it s easier to follow for learning  Rounding at the end  of course  is optional       private long remap long p  long Amin  long Amax  long Bmin  long Bmax          double deltaA   Amax - Amin      double deltaB   Bmax - Bmin      double scale    deltaB   deltaA      double negA     -1   Amin      double offset    negA   scale    Bmin      double q         p   scale    offset      return Math round q

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That s a simple linear conversion   new value      old value - old min     old max - old min       new max - new min    new min   So converting 10000 on the scale of -16000 to 16000 to a new scale of 0 to 100 yields   old value   10000 old min   -16000 old max   16000 new min   0 new max   100  new value       10000 - -16000      16000 - -16000       100 - 0    0             81 25

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There is a condition  when all of the values that you are checking are the same  where  jerryjvl s code would return NaN   if  OldMin    OldMax  amp  amp  NewMin    NewMax       return    OldValue - OldMin     NewMax - NewMin      OldMax - OldMin     NewMin else      return  NewMax   NewMin    2

[python] Convert a number range to another range, maintaining ratio

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